\(F_\rho=-\cfrac{\partial\,\psi}{\partial\,x}\)
This force act against the system and results in work done that is equal to a change in energy \(\psi\). So, the resistance exerted by the system of a solitary particle on an external agent is given by,
\(F_i=-F_\rho=\cfrac{\partial\,\psi}{\partial\,x}\)
where \(F_i\) is the force exerted by the particle on an external agent. So,
\(F_i=-F_{\rho}=-i\sqrt { 2{ mc^{ 2 } } }\,G.tanh\left( \cfrac { G }{ \sqrt { 2{ mc^{ 2 } } } } (x-x_z) \right)\)
The following diagram shows the interaction between two monopoles of positive \(F_i\), ie (-\(F_\rho\))
The concentration of \(\psi\) between the two particles pushes them apart. And their interaction is thus repulsive.
In a similar way, the diagram below shows the interaction between two monopoles of \(-F_i\), ie (+\(F_\rho\))
The depletion of \(\psi\) between the two particles pulls them together. And their interaction is thus attractive.
Both diagrams show \(F_{\rho}\), the force developed in previous posts, from an external agent affecting a change in \(\psi\) around the particle. Strictly speaking the force due to the particles are,
And the interaction of two dissimilar particles is,
If the interaction of two positive \(F_i\) is that of charges (repulsive, like charges repel) and the interaction of two \(-F_i\) is that of gravity particle (attractive, two masses attract), then the interaction of \(F_i\) and \(-F_i\) shown above, is attractive as though the charge has mass; the interaction between two masses is attractive.
If the interaction of \(+F_i\) is that of negative charges, then along the negative \(t_c\) time dimension we have positive charges. Similarly, along \(-t_g\) time dimension, anti-mass particles.
Negative and positive charges are matter/anti-matter pair, and mass and anti-mass are similarly matter/anti-matter pair.
